Modeling Biogeochemical Cycles: Dynamical Climatology Gerrit Lohmann 2. June 2005, 15.15 o‘clock...
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Transcript of Modeling Biogeochemical Cycles: Dynamical Climatology Gerrit Lohmann 2. June 2005, 15.15 o‘clock...
Modeling Biogeochemical Cycles: Dynamical Climatology
Gerrit Lohmann2. June 2005, 15.15 o‘clock
• Biogeochemical cycles• Clocks 14-C• Thermohaline Circulation• Some homework
Modeling Biogeochemical Cycles:
Turnover Time, renewal time
M content if a substance in the reservoir
S total flux out of the reservoir
MS=kMQ
single reservoir with source flux Q, sink flux S, and content M
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The turnover time of carbon in biota in the ocean surface water is3 x 1015/(4+36) x 1015yr ≈ 1 month
The equation describing the rate of change of the content of a reservoir can be written as
Modeling Biogeochemical Cycles:
If the reservoir is in a steady state (dM/dt = 0) then the sources (Q) and sinks (S) must balance.
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If material is removed from the reservoir by two or more separate processes, each with a flux Si, then turnover times with respect to each process can be defined as:
Since ∑ Si = S, these time scales are related to the turnover time of the reservoir,
In fluid reservoirs like the atmosphere or the ocean, the turnover time of a tracer is also related to the spatial and temporal variability of its concentration within the reservoir.
Modeling Biogeochemical Cycles:
Fig. 4-2 Inverse relationship between relative stand-dard deviation of atmospheric concentration and turnover time for important trace chemicals in thetroposphere. (Modified from Junge (1974) with per-mission from the Swedish Geophysical Society.)
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In fluid reservoirs like the atmosphere or the ocean, the turnover time of a tracer is also related to the spatial and temporal variability of its concentration within the reservoir.
Modeling Biogeochemical Cycles:
Atmosphere 725(Annual increase ~3)
Surface waterDissolved inorg. 700
Dissolved org. 25(Annual increase ~ 0,3)
Surface biota3
Intermediate andDeep water
Dissolved inorg. 36,700Dissolved org. 975
(Annual increase ~ 2,5)
Short-lived biota~110
Long-lived biota ~450(Annual decrease ~1)
Litter~60
Soil 1300 - 1400(Annual decrease ~1)
Peat (Torf)~160
Fossil fuelsoil, coal, gas
5,000 - 10,000
Respiration &decomposition
~36
Primaryproduction
~40
Detritus~4
Detritus decomposition
54-50
~40 ~38
5
2 - 5
2 - 5
~15~40
~120~60~90~93Deforestation
~1
‹1
‹1
~15~1
Fig. 4-3 principal reservoirs and fluxes in the carbon cycle. Units are 1015 g(Pg) C (burdens)and PgC/yr (fluxes). (From Bolin (1986) with permission from John Wiley and Sons.)
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Modeling Biogeochemical Cycles:
The residence time is the time spent in a reservoir by an individual atom or molecule. It is also theage of a molecule when it leaves the reservoir. PDF
PDF of residence times be denoted by ø ( )
The (average) residence time
The (average) age of atoms in a reservoir is given by[PDF is always decreasing ]
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lake
exponential decay238 U
removal is biasedtowards young particles"short circuit" case:Sink close to the source
Modeling Biogeochemical Cycles: The adjustment process is
e-folding time
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Modeling Biogeochemical Cycles:
The flux Fij from reservoir i to reservoir j is given by
The rate of change of the amount Mi in reservoir i is thus
where n is the total number of reservoirs in the system. This system of differential equationscan be written in matrix form as
where the vector M is equal to (M1, M2,... Mn) and the elements of matrix k are linear combinationsof the coefficients kij
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Modeling Biogeochemical Cycles: 4 - 6
Modeling Biogeochemical Cycles:
where and are the eigenvectors of the matrix k. In our case we have
or, in component form and in terms of the initial conditions:
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Modeling Biogeochemical Cycles: 4 - 6
response time
cycle 1k12 k21
turnover times of the two reservoirs
cycle
1
01
1
02
1
Modeling Biogeochemical Cycles:
?
Modeling Biogeochemical Cycles:
ATMOSPHERE (dust)
SURFACE OCEAN
SEDIMENTS
2812
0.00009
1.29X108
DEEP OCEAN
MINE-RABLE
P
323-645
6460OCEAN BIOTA
87.5Land (upper 60 cm of soil)
96.9
LAND BIOTA
1.6 - 4.032.2
0.11
1.870.58 1.4
0.690.600.39
0.02 0.010.140.106.06.0
The global phosphorus cycle. Values shown are in Tmol and Tmol/yr. (T=10^12)The mass of P in each reservoir and rates of exchange. Phosphate PO4(3-)
33.6
0.03
0.10
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Modeling Biogeochemical Cycles:
Table 4-1 Response of phosphorus cycle to mining output. Phosphorus amounts are given inTg P (1Tg=1012g). In addition, a pertubation is introduced by the flux from reservoir 7 (mineablephosphorus), which is given by 12 exp(0.07t) in units of Tg P/yr
Tcycle = 5300 years
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Modeling Biogeochemical Cycles:
Q T
S1 S2
1 2
Example: An open two-reservoir system
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Modeling Biogeochemical Cycles:
Simplified model of the carbon cycle. Ms represents the sum of all forms ofdissolved carbon , , and
CO2
H 2 HCO3
HCO3
,
CO 22
Atmosphere
M A
Terrestrial System
M T
Ocean surfaceDiss C= CO2,HCO3,H2CO3
M S
Deep layers of ocean
M D
F TA
F AT
F SA F AS
F SDF DS
Non-linear System: Simplified model of the biogeochemical carbon cycle. (Adapted from Rodhe and Björkström (1979) with the permission of the Swedish Geophysical Society.)
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Modeling Biogeochemical Cycles:
where the exponent SA (the buffer, or Revelle factor) is about 9. The buffer
factor results from the equilibrium between CO2(g) and the more prevalent forms of
dissolved carbon. As a consequence of this strong dependence of FSA on MS,
a substantial increase in CO2 in the atmosphere is balanced by a small increase of MS.
FSA kSAM S
SA
FAT K AT M AAT
FAT K AT M AAT
atmosphere to the terrestial system
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Modeling Biogeochemical Cycles: 4 - 12
uptake of atmospheric CO2 by terrestrial biota
with MTB being the content of carbon in terrestrial biota and D, a Michaelis constant.Mass MTB may grow without bounds. To avoid such a mathematical explosion, Williams(1987) suggested that the factor MTB in Equation (33) be replaced by
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Fig. 4.13 Calculated and observed annual wet deposition of sulfur in mgS/m2 per year.
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Modeling Biogeochemical Cycles:
ThermodynamicEquation
Equationsof Motion
TurbulenceParameterization
SaltEquation
Sea Ice
ThermodynamicEquation
HydrologicEquation
Vegetation
Land Ice
OCEAN LAND
TurbulenceParameterization
Equationsof Motion
Radiation
ThermodynamicEquation
WaterConservation
Equation
CloudParameterization
ATMOSPHERE
Sensible Heat
Radiation
Runoff
WindStress
Sensible Heat
Radiation
Evaporation
Precipitation
Evaporation
Precipitation
Schematic diagram showing the components of a global climate model (GCM).
4 - 14
Modeling Biogeochemical Cycles:
organized fluid motion molecular diffusion
continuity of tracer mass
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Modeling Biogeochemical Cycles: 4 - 14
Eddy correlation technique, eddy diffusivity
Modeling Biogeochemical Cycles:
Fig 4-15 Orders of magnitude of the average vertical molecular or turbulent diffusivity(which is largest) through the atmosphere, oceans, and uppermost layer of ocean sediments.
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Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles:
Modeling Biogeochemical Cycles: